The resistance of a wire is inversely proportional to the square of its diameter. If an AWG (American wire gauge) size 12 conductor (0.0808-in. diameter) has a resistance of 14.8, what will be the resistance of an AWG size 10 conductor (0.1019-in. diameter) of the same length and material?
R = (0.0808/0.1019)^2 * 14.8=9.31 Ohms.
To determine the resistance of the AWG size 10 conductor, we need to use the information provided about the resistance and diameter of the AWG size 12 conductor.
Let's first define the relationship between resistance and the diameter of a wire. We are given that the resistance of a wire is inversely proportional to the square of its diameter. This means that as the diameter decreases, the resistance increases, and vice versa.
We can express this relationship mathematically as:
Resistance ∝ 1 / (Diameter)^2
Now, let's use the information given to relate the resistance and diameter of the two wire sizes.
1. First, we need to find the resistance constant (k) for the AWG size 12 wire. We can do this by rearranging the equation:
Resistance = k / (Diameter)^2
Given that the diameter of the AWG size 12 wire is 0.0808 inches and the resistance is 14.8, we can substitute these values into the equation:
14.8 = k / (0.0808^2)
Solving for k, we have:
k = 14.8 * 0.0808^2
2. Now that we have the resistance constant (k), we can find the resistance of the AWG size 10 wire. Again, we'll use the equation:
Resistance = k / (Diameter)^2
Given that the diameter of the AWG size 10 wire is 0.1019 inches, we can substitute these values into the equation:
Resistance = k / (0.1019^2)
Substituting the value of k that we found earlier, we have:
Resistance = (14.8 * 0.0808^2) / (0.1019^2)
Calculating this expression will give us the resistance of the AWG size 10 conductor.
Please note that the resistance is often measured in units such as ohms (Ω), so make sure to check the units of the given resistance value and use the appropriate units in your calculations.